   Chapter 1.2, Problem 91E

Chapter
Section
Textbook Problem

Quality Control PAR Manufacturing manufactures steel rods. Suppose the rods ordered by a customer are manufactured to a specification of 0.5 in. and are acceptable only if they are within the tolerance limits of 0.49 in. and 0.51 in. Letting x denote the diameter of a rod, write an inequality using absolute value signs to express a criterion involving x that must be satisfied in order for a rod to be acceptable.

To determine

To discuss: The inequality using absolute value sign to satisfy the criteria for the given specification.

Explanation

Given:

The specification of rod is 0.5 in and the tolerance limits are 0.49 in and 0.51 in.

Calculation:

The absolute value of a number a is denoted by |a| and is defined as,

|a|={aifa0aifa<0

Let x denote the diameter of rod, the specification of rod is 0.5 in and the tolerance limits are 0.49 in and 0.51 in, the absolute value inequality of x is,

|x0.5|0.01

To check the inequality satisfies the criteria, expand the absolute value function from the definition of absolute value. The equations becomes,

|x0.5|={(x0.5)if(x0.5)0(x0.5)if(x0.5)<0

For (x0.5)0 , the expression becomes,

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